CHAOS
Making a New Science
James Gleick
To Cynthia
human was the music,
natural was the static…
—JOHN UPDIKE
Contents
Prologue
The Butterfly Effect
Edward Lorenz and his toy weather. The computer misbehaves. Long-range forecasting is doomed. Order masquerading as randomness. A world of nonlinearity. “We completely missed the point.”
Revolution
A revolution in seeing. Pendulum clocks, space balls, and playground swings. The invention of the horseshoe. A mystery solved: Jupiter’s Great Red Spot.
Life’s Ups and Downs
Modeling wildlife populations. Nonlinear science, “the study of non-elephant animals.” Pitchfork bifurcations and a ride on the Spree. A movie of chaos and a messianic appeal.
A Geometry of Nature
A discovery about cotton prices. A refugee from Bourbaki.

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For the young physicists and mathematicians leading the revolution, a starting point was the Butterfly Effect.
The Butterfly
Effect
Physicists like to think that all you have to do is say, these are the conditions, now what happens next?
—RICHARD P. FEYNMAN
THE SUN BEAT DOWN through a sky that had never seen clouds. The winds swept across an earth as smooth as glass. Night never came, and autumn never gave way to winter. It never rained. The simulated weather in Edward Lorenz’s new electronic computer changed slowly but certainly, drifting through a permanent dry midday midseason, as if the world had turned into Camelot, or some particularly bland version of southern California.
Outside his window Lorenz could watch real weather, the early-morning fog creeping along the Massachusetts Institute of Technology campus or the low clouds slipping over the rooftops from the Atlantic.

…

Given a slightly different starting point, the weather should unfold in a slightly different way. A small numerical error was like a small puff of wind—surely the small puffs faded or canceled each other out before they could change important, large-scale features of the weather. Yet in Lorenz’s particular system of equations, small errors proved catastrophic.
HOW TWO WEATHER PATTERNS DIVERGE. From nearly the same starting point, Edward Lorenz saw his computer weather produce patterns that grew farther and farther apart until all resemblance disappeared. (From Lorenz’s 1961 printouts.)
He decided to look more closely at the way two nearly identical runs of weather flowed apart. He copied one of the wavy lines of output onto a transparency and laid it over the other, to inspect the way it diverged. First, two humps matched detail for detail.

pages: 360words: 85,321

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling
by
Adam Kucharski

According to Neil Johnson, who led the research, these events are a world away from the kind of situations covered by traditional financial theories. “Humans are unable to participate in real time,” he said, “and instead, an ultrafast ecology of robots rises up to take control.”
WHEN PEOPLE TALK ABOUT chaos theory, they often focus on the physics side of things. They might mention Edward Lorenz and his work on forecasting and the butterfly effect: the unpredictability of the weather, and the tornado caused by the flap of an insect’s wings. Or they might recall the story of the Eudaemons and roulette prediction, and how the trajectory of a billiard ball can be sensitive to initial conditions. Yet chaos theory has reached beyond the physical sciences. While the Eudaemons were preparing to take their roulette strategy to Las Vegas, on the other side of the United States ecologist Robert May was working on an idea that would fundamentally change how we think about biological systems.

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Poincaré argued that a difference in the starting state of a roulette ball—one so tiny it escapes our attention—can lead to an effect so large we cannot miss it, and then we say that the effect is down to chance.
The problem, which is known as “sensitive dependence on initial conditions,” means that even if we collect detailed measurements about a process—whether a roulette spin or a tropical storm—a small oversight could have dramatic consequences. Seventy years before mathematician Edward Lorenz gave a talk asking “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” Poincaré had outlined the “butterfly effect.”
Lorenz’s work, which grew into chaos theory, focused chiefly on prediction. He was motivated by a desire to make better forecasts about the weather and to find a way to see further into the future. Poincaré was interested in the opposite problem: How long does it take for a process to become random? In fact, does the path of a roulette ball ever become truly random?

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Without hops, the company could expect beer to last between twelve and seventeen days; adding the right amount of hops could increase the life span by several weeks.
Betting teams aren’t particularly interested in knowing why certain factors are important, but they do want to know how good their predictions are. It might seem easiest to test the predictions against the racing data the team had just analyzed. Yet this would be an unwise approach.
Before he worked on chaos theory, Edward Lorenz spent the Second World War as a forecaster for the US Air Corps in the Pacific. One autumn in 1944, his team made a series of perfect predictions about weather conditions on the flight path between Siberia and Guam. At least they were perfect according to the reports from aircraft flying that route. Lorenz soon realized what was causing the incredible success rate. The pilots, busy with other tasks, were just repeating the forecast as the observation.

Indeed, you could have said that about Tunisia, Egypt, and several other countries for decades. They may have been powder kegs but they never blew—until December 17, 2010, when the police pushed that one poor man too far.
In 1972 the American meteorologist Edward Lorenz wrote a paper with an arresting title: “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” A decade earlier, Lorenz had discovered by accident that tiny data entry variations in computer simulations of weather patterns—like replacing 0.506127 with 0.506—could produce dramatically different long-term forecasts. It was an insight that would inspire “chaos theory”: in nonlinear systems like the atmosphere, even small changes in initial conditions can mushroom to enormous proportions. So, in principle, a lone butterfly in Brazil could flap its wings and set off a tornado in Texas—even though swarms of other Brazilian butterflies could flap frantically their whole lives and never cause a noticeable gust a few miles away.

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He meant that if that particular butterfly hadn’t flapped its wings at that moment, the unfathomably complex network of atmospheric actions and reactions would have behaved differently, and the tornado might never have formed—just as the Arab Spring might never have happened, at least not when and as it did, if the police had just let Mohamed Bouazizi sell his fruits and vegetables that morning in 2010.
Edward Lorenz shifted scientific opinion toward the view that there are hard limits on predictability, a deeply philosophical question.4 For centuries, scientists had supposed that growing knowledge must lead to greater predictability because reality was like a clock—an awesomely big and complicated clock but still a clock—and the more scientists learned about its innards, how the gears grind together, how the weights and springs function, the better they could capture its operations with deterministic equations and predict what it would do.

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These are false dichotomies, the first of many we will encounter. We live in a world of clocks and clouds and a vast jumble of other metaphors. Unpredictability and predictability coexist uneasily in the intricately interlocking systems that make up our bodies, our societies, and the cosmos. How predictable something is depends on what we are trying to predict, how far into the future, and under what circumstances.
Look at Edward Lorenz’s field. Weather forecasts are typically quite reliable, under most conditions, looking a few days ahead, but they become increasingly less accurate three, four, and five days out. Much beyond a week, we might as well consult that dart-throwing chimpanzee. So we can’t say that weather is predictable or not, only that weather is predictable to some extent under some circumstances—and we must be very careful when we try to be more precise than that.

“Jobs at the top universities were filled . . .”: For an example of the kind of recommendation I have in mind, see Wheeler (2011). This letter is the origin of the quote “best men” in the next sentence.
“. . . Silver City was a paradigm Western mining town”: This background on Silver City is from Wallis (2007).
“. . . first developed by a man named Edward Lorenz”: The biographical and historical details concerning Lorenz and the history of chaos theory are from Gleick (1987) and Lorenz (1993).
“. . . the work of two physicists named James Yorke and Tien-Yien Li . . .”: The article is Li and Yorke (1975).
“. . . the so-called butterfly effect . . .”: The paper is Lorenz (2000). Lorenz never used the metaphor of a butterfly flapping its wings, though he sometimes used a similar metaphor involving a seagull

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He got in, and instead of finishing high school in Silver City, he moved into Ingerson’s attic in Moscow, Idaho, to start his career as a physicist. After a year in Idaho, though, Farmer was ready for bigger pastures. In 1970, he transferred to Stanford University. True to his ambitions, he majored in physics — laying the groundwork for a career that would change science, and finance, forever.
The ideas at the heart of Farmer’s and Packard’s work were first developed by a man named Edward Lorenz. As a young boy, Lorenz thought he wanted to be a mathematician. He had a clear talent for mathematics, and when it came time to select a major at Dartmouth, he had few doubts about what he would choose. He graduated in 1938 and went on to Harvard, planning to pursue a PhD. But World War II interfered with his plans: in 1942, he joined the U.S. Army Air Corps. His job was to predict the weather for Allied pilots.

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It is tempting to say that Farmer, Packard, and their Prediction Company collaborators “used chaos theory to predict the markets” or something along those lines. In fact, this is how their enterprise is usually characterized. But that isn’t quite right. Farmer and Packard didn’t use chaos theory as a meteorologist or a physicist might. They didn’t do things such as attempt to find the fractal geometry underlying markets, or derive the deterministic laws that govern financial systems.
Instead, the fifteen years that Farmer and Packard spent working on chaos theory gave them an unprecedented (by 1991 standards) understanding of how complex systems work, and the ability to use computers and mathematics in ways that someone trained in economics (or even in most areas of physics) would never have imagined possible. Their experience with chaos theory helped them appreciate how regular patterns — patterns with real predictive power — could be masked by the appearance of randomness.

The mathematics of dynamic self‐regulating systems frequently involves differential equations that are difficult or impossible to solve by traditional methods. It is too easy to slip into the practice of making what are called ‘linearizing approximations’, and then forget their presence as the model evolves.
Scientists of these separated disciplines should have realized that they were on the wrong track when quite independently the geophysicist Edward Lorenz, in 1961, and the neo‐Darwinist biologist Robert May, in 1973, made the remarkable discovery that deterministic chaos was an inherent part of the computer models they researched. Deterministic chaos is not an oxymoron, however much it may seem like one. Up until Lorenz and May started using computers to solve systems rich in difficult equations almost all science clung to the comforting idea put forward in 1814 by the French mathematician Pierre‐Simon Laplace that the universe was deterministic and if the precise location and momentum of every particle in the universe were known, then by using Newton’s laws we could reveal the entire course of cosmic events, past, present and future.

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It took the discovery of the utter incomprehensibility of quantum phenomena to force the acceptance of a statistical more than a deterministic world; this was later consummated by the discoveries that came from the availability of affordable computers. These have enabled scientists to explore the world of dynamics – the mathematics of moving, flowing and living systems. The insights from the numerical analysis of fluid dynamics by Edward Lorenz and of population biology by Robert May revealed what is called ‘deterministic chaos’. Systems like the weather, the motion of more than two astronomical bodies linked by gravitation, or more than two species in competition, are exceedingly sensitive to the initial conditions of their origin, and they evolve in a wholly unpredictable manner. The study of these systems is a rich and colourful new field of science enlivened by the visual brilliance of the strange images of fractal geometry.

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Vernadsky expanded the definition of biosphere to include the concept that life is an active participant in geological evolution, encapsulating this notion in the phrase, ‘Life is a geological force.’ Vernadsky was following a tradition set by Darwin, Huxley, Lotka, Redfield and many others, but unlike them his ideas were mostly anecdotal. Biosphere is now mainly used, in Vernadsky’s sense, as an imprecise word that acknowledges the power of life on Earth without surrendering human sovereignty.
CHAOS THEORY
Certainty and confidence in science marked its development in the nineteenth and much of the twentieth centuries, but now it carries on unaware that the determinism that had so long enlivened it is dead. The recognition that science was provisional and could never be certain was always there in the minds of good scientists. The nineteenth‐century application of statistics, first in commerce then in science, made probabilistic thinking more intelligible than faith‐based certainties.

If you make a certain decision one morning on your way to work, like pausing for a second before crossing the road, then you might miss the opportunity of bumping into an old friend who gives you some information that leads to your applying for a new job that changes your life; a split second later still in crossing that road and you could be hit by a bus. Our destiny may be mapped out for us in a deterministic universe, but it is totally unpredictable.
The man who first brought these ideas to the world and in doing so helped create the new concept of chaos was Edward Lorenz, an American mathematician and meteorologist who hit upon the phenomenon by accident while he was working on modeling weather patterns in the early 1960s. He was using an early “desktop” computer, the LGP-30, to run his simulation. At one point he wanted to repeat a simulation by running the computer program again with identical inputs. To do this he used a number the computer had calculated and printed out halfway through its run.

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Chaos is not really a theory as such (although “chaos theory” has become a commonly used term, and I still plan to use it). It is a concept, or phenomenon, that we find to be almost ubiquitous in nature and has spawned a whole new discipline in science with the rather less imaginative title of nonlinear dynamics—a description which derives from the main mathematical property of chaotic systems, namely that cause and effect are not related in a linear, proportional way. By this I mean that it had been assumed before chaos was fully understood that, while effect must follow cause, simple causes would always lead to simple effects and complex causes to complex effects. The notion that a simple cause could lead to a complex effect was quite unexpected. This is what mathematicians mean by “nonlinear.”
Chaos theory tells us that order and determinism can breed what appears to be randomness.

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The answer, I believe, despite what I have said about determinism, is yes, we still do. And it is rescued not by quantum mechanics, as some physicists argue, but by chaos theory. For it doesn’t matter that we live in a deterministic universe in which the future is, in principle, fixed. That future would be knowable only if we were able to view the whole of space and time from the outside. But for us, and our consciousnesses, embedded within space-time, that future is never knowable to us. It is that very unpredictability that gives us an open future. The choices we make are, to us, real choices, and because of the butterfly effect, tiny changes brought about by our different decisions can lead to very different outcomes, and hence different futures.
So, thanks to chaos theory, our future is never knowable to us. You might prefer to say that the future is preordained and that our free will is just an illusion—but the point remains that our actions still determine which of the infinite number of possible futures is the one that gets played out.

If you connect the links one way, you will
track the following movement:
Cubism
 Suprematism  Constructivism  Bauhaus
Follow another line, and you will get to the Bauhaus this way:
Synthetism
 Fauvism  Expressionism  Bauhaus
Barr’s chart is a teleological document that culminates with the
presentation of these objects in MOMA’s galleries. The exactitude of Barr’s chart is unlikely to emerge from the process of
bespoke futures. The skewing of the classic scenario-building
process undermines such vectoral surety and ﬁxed relationships.
Instead, a better model might be found in the dynamic imagescapes of the Lorenz strange attractor, one of the earliest and
still most potent visualizations of chaotic systems.26 Edward
Lorenz, a mathematician and meteorologist at MIT, needed a
new way to analyze atmospheric conditions. He came up with
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CHAPTER 5
a dynamic model in which seemingly random and chaotic outliers were eventually contained within a deﬁnite ﬁgure (often
described as looking like an owl’s eyes) in which solutions
approach but do not replicate each other exactly. The equations are described as deterministic, yet they are extremely
sensitive to their initial conditions.

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A minor change in the original condition can effect a hugely
different outcome—better known as the “butterﬂy effect”—and
can also create a different attractor, collapsing it into a ﬁxed
solution or tumbling it back into apparent chaos before a new
strange attractor establishes itself. This effect is readily visible
when you watch an animation of the strange attractor, many
of which are now available on the World Wide Web. Disequilibrium can fall into a dynamic equilibrium with a slight shift, and
can again be thrown into a new disequilibrium by yet another
shift. The strange attractor can be any point within an orbit
that appears to pull the entire system toward it.
Chaos theory is based in part on the fact that Newtonian paradigms of predictability do not actually work. Accepting nonlinear
systems creates a challenge to scenario planning. Recasting
scenario planning to create bespoke futures acknowledges the
unpredictability of strange attractors, but hopes to use the
process itself (as well as its result) to move the system toward
a tipping point. Returning to Barr’s diagram, bespoke futures
are more like strange attractors than oppositional or political avant-gardist objects.27 The bespoke futures process can
develop attractors to pull the entire system toward new and
more hopeful visions of worlds to come.

We have discussed emergent behavior, where small local rules result in complex, macro-level, group behavior. The pattern we have observed here, rather than emergent behavior, can be classified as a kind of “butterfly effect”; see the sidebar Butterfly Effect.
Figure 8-6. Population fluctuation swings, resulting in extinction of the roids
Butterfly Effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change somewhere in a nonlinear system can result in large differences at a later stage. This name was coined by Edward Lorenz, one of the pioneers of chaos theory (and no relation to Max Lorenz of the Lorenz curve fame).
In 1961, Lorenz was using a computer model to rerun a weather prediction when he entered the shortened decimal value .506 instead of entering the full .506127. The result was completely different from his original prediction.

The mathematical system may be demonstrably incomplete, and the world might not be pinned down on the
fringes, but for all practical purposes the world can be known.
Unfortunately, while “almost” might work for horseshoes and hand
grenades, 30 years after Godel and Heisenberg yet a third limitation of our
knowledge was in the wings, a limitation that would close the door on any
attempt to block out the implications of microscopic uncertainty on predictability in our macroscopic world. Based on observations made by Edward Lorenz in the early 1960s and popularized by the so-called butterfly
effect—the fanciful notion that the beating wings of a butterfly could
change the predictions of an otherwise perfect weather forecasting system—this limitation arises because in some important cases immeasurably
small errors can compound over time to limit prediction in the larger
scale. Half a century after the limits of measurement and thus of physical
knowledge were demonstrated by Heisenberg in the world of quantum
mechanics, Lorenz piled on a result that showed how microscopic errors
could propagate to have a stultifying impact in nonlinear dynamic systems.

…

Half a century after the limits of measurement and thus of physical
knowledge were demonstrated by Heisenberg in the world of quantum
mechanics, Lorenz piled on a result that showed how microscopic errors
could propagate to have a stultifying impact in nonlinear dynamic systems.
This limitation could come into the forefront only with the dawning of the
computer age, because it is manifested in the subtle errors of computational accuracy.
The essence of the butterfly effect is that small perturbations can have
large repercussions in massive, random forces such as weather. Edward
Lorenz was a professor of meteorology at MIT, and in 1961 he was testing
and tweaking a model of weather dynamics on a rudimentary vacuumtube computer. The program was based on a small system of simultaneous
equations, but seemed to provide an inkling into the variability of weather
patterns. At one point in his work, Lorenz decided to examine in more detail one of the solutions he had generated. To save time, rather than starting the run over from the beginning, he picked some intermediate
conditions that had been printed out by the computer and used those as
the new starting point.

…

For his
application in the narrow scientific discipline of weather prediction, this
meant that no matter how precise the starting measurements of weather
conditions, there was a limit after which the residual imprecision would
lead to unpredictable results, so that “long-range forecasting of specific
weather conditions would be impossible.” And since this occurred in a
very simple laboratory model of weather dynamics, it could only be worse
in the more complex equations that would be needed to properly reflect
the weather. Lorenz discovered the principle that would emerge over time
into the field of chaos theory, where a deterministic system generated with
simple nonlinear dynamics unravels into an unrepeated and apparently
random path.
The simplicity of the dynamic system Lorenz had used suggests a farreaching result: Because we cannot measure without some error (harking
back to Heisenberg), for many dynamic systems our forecast errors will
grow to the point that even an approximation will be out of our hands.

Zoom again, and yet more fine detail emerges. You can do this forever, and at each stage get an entirely different picture. Its study has become a classic problem in pure mathematics.
The Mandelbrot set belongs to both fractal geometry and chaos theory. A chaotic system, far from being disorganized or non-organized, starts with one particular point and cranks it through a repeating process; the outcome is unpredictable if you do not know the process—and it depends heavily on the starting point. The most famous example of chaos was proposed by meteorologist Edward Lorenz in 1972: Can the flap of a butterfly’s wings in Brazil set off a tornado in Texas? The basic idea is that if you stand a pencil on its point and let it fall through force of gravity, exactly where it lands depends on where it began, whether it was leaning infinitesimally in one direction or another.

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Studying roughness, Mandelbrot found fractal order where others had only seen troublesome disorder. His manifesto, The Fractal Geometry of Nature, appeared in 1982 and became a scientific bestseller. Soon, T-shirts and posters of his most famous fractal creation, the bulbous but infinitely complicated Mandelbrot Set, were being made by the thousands. His ideas were also embraced immediately by another scientific movement, chaos theory. “Fractals” and “chaos” entered the popular vocabulary. In 1993, on receiving the prestigious Wolf Prize for Physics, Mandelbrot was cited for “having changed our view of nature.”
MANDELBROT’S LIFE story has been a tale of roughness, irregularity,. and what he calls “wild” chance. He was born in Warsaw in 1924, and tutored privately by an uncle who despised rote learning; to this day, Mandelbrot says, the alphabet and times tables trouble him mildly.

…

My key contribution was to found a new branch of mathematics that perceives the hidden order in the seemingly disordered, the plan in the unplanned, the regular pattern in the irregularity and roughness of nature. This mathematics, called fractal geometry, has much to say in the natural sciences. It has helped model the weather, study river flows, analyze brainwaves and seismic tremors, and understand the distribution of galaxies. It was immediately embraced as an essential mathematical tool in the 1980s by “chaos” theory, the study of order in the seeming-chaos of a whirlpool or a hurricane. It is routinely used today in the realm of man-made structures, to measure Internet traffic, compress computer files, and make movies. It was the mathematical engine behind the computer animation in the movie, Star Trek II: the Wrath of Khan.
I believe it has much to contribute to finance, too. For forty years in fits and starts, as allowed by my personal interests, by unfolding events, and by the availability of colleagues to talk to, the development of fractal geometry has continually interacted with my studies of financial markets and economic systems.

Traditional economics assumed perfectly rational agents. So does traditional survival training. Neither assumption reflects the messy real world.
The idea of chaos theory is that what appears to be a very complex, turbulent system (the weather, for example) can begin with simple components (water, air, earth), operating under a few simple rules (heat and gravity). One of the characteristics of such a system is that a small change in the initial conditions, often too small to measure, can lead to radically different behavior. Run the equations two, four, eight times, and they may seem to be giving similar results. But the harder you drive the system, the more iterations result and the more unpredictable it becomes.
Edward Lorenz, a meteorologist at MIT, was modeling weather systems on a computer in the early 1960s when he accidentally discovered that a tiny change in the initial state (1 part in 1,000) was enough to produce totally different weather patterns.

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Just when you think you’ve found the smallest piece, you find another even smaller one.
The theory of self-organized criticality, sometimes called Complexity theory, was developed hard on the heels of chaos theory by some of the same people. It asked and suggested answers to questions as fundamental as: Where does order come from? How do you reconcile it with the second law of thermodynamics, which says that everything is heading toward more disorder? In a sense, complexity was an extension of the thinking that gave rise to chaos theory; indeed, it was often referred to as existing at “the edge of chaos.” (There has also been strong objection to linking complexity and chaos and to using the term “complexity.”) Like chaos theory, complexity theory postulated “upheaval and change and enormous consequences flowing from trivial-seeming events—and yet with a deep law hidden beneath.”

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(For that matter, if they had not misperceived which way was down, they might not have positioned themselves over Hillman and Biggs.) But the accident was still no one’s fault. There is no cause for such system accidents in the traditional sense, no blame, as the I Ching says. The cause is in the nature of the system. It’s self-organizing.
WHEN NORMAL ACCIDENTS was published, neither chaos theory nor the theory of self-organizing systems was widely known or accepted. But it is possible to see hints of both in Perrow’s work. Chaos theory arose out of a huge vacuum in the physical sciences: disorder. We see it everywhere we look, from the functioning of a living organism to the behavior of flowing water: turbulence; erratic behavior; nonperiodic natural cycles from weather to animal populations. Classical physics ignored all that and used idealized systems to explain the world.

What difference does that make in your system?’ He wasn’t trying to catch us out; he was trying to grasp what we do. I was never able to explain to his satisfaction that it all depends. Is this a change that can be made without altering any of the other variables that the neural network ranks upon? Very seldom is there a movie where any significant alteration doesn’t mean changes elsewhere.” To modify a phrase coined by chaos theory pioneer Edward Lorenz, a butterfly that flaps its wings in the first minute of a movie may well cause a hurricane in the middle of the third act.
The studio boss to whom Meaney refers was likely picking a purposely arbitrary detail by mentioning the color of a character’s shirt. After all, who ever formed their opinion about which movie to go and see on a Saturday night, or which film to recommend to friends, on the basis of whether the protagonist wears a blue shirt or a red shirt?

The data, one might think, would be adequate: more than ten thousand weather stations check conditions around the globe, another five thousand ships and planes send in information, unmanned buoys transmit data from remote reaches of the world’s oceans, more than a thousand weather balloons go up each day to sample the sky, and satellites circle endlessly with their gaze turned back toward earth. But the data are not adequate. In 1963, Edward Lorenz set up weather models on a computer. He compared models run with data offering three decimal points of accuracy and those run with data offering six decimal points of accuracy. The results were completely different. Tiny differences in the starting point resulted in major differences at the end point. It would be comparable to a banker counting his wealth in dollars and in pennies, only to discover that he was well positioned in dollars but flat broke in pennies. It made no sense. It led to what was later called chaos theory. Lorenz delivered a talk to the American Academy for the Advancement of Science titled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”

…

This so-called Richardson effect is often ignored in technical papers attempting to relate shoreline length to various ecological phenomena and political or economic statistics.
Some sources suggest that Lorenz had planned to mention a seagull’s wings rather than a butterfly’s wings. Lorenz was swayed to the butterfly by another meteorologist, Philip Merilees. The ideas expressed in the talk — intended to explain why accurate weather forecasting is so challenging — led to a blossoming of the much-misunderstood chaos theory, popularized in books and movies, including Jurassic Park. The essence of chaos theory is that small differences in initial conditions can result in huge differences in subsequent outcomes. Lorenz died on April 16, 2008, at age ninety.
James Glaisher wrote a full account of his balloon ascent, published on September 5, 1862, as “Greatest Height Ever Reached” in the British Association Report (1862, pp. 383–85). During the ascent, Glaisher describes himself fading in and out of consciousness at high altitudes.

Having to create our own incentives—finishing the “I shall . . .” statement by making commitments to ourselves. And that process begins by knowing who you are and, perhaps more important, how you feel.
Flap Your Wings
For every intervention you adopt, you create change. This was articulated beautifully by the late Edward Lorenz: when a butterfly flutters its wings in one part of the world, it can eventually cause a hurricane in another. Lorenz was an MIT meteorologist who tried to explain why it is so hard to make good weather forecasts; he wound up starting a scientific revolution called chaos theory. In the early 1960s, he noticed that small differences in a dynamic system such as the atmosphere could give rise to vast and often unexpected results. These observations ultimately led him to develop what became known as the butterfly effect, a term that grew out of an academic paper he presented in 1972 entitled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”

The reason for this, viewed from the standpoint of classical physics, is that accurately measuring the position of an electron requires illuminating the electron with light of a very short wavelength. The shorter the wavelength the greater the amount of energy that hits the electron and the more accurate the measurement, but the greater the energy hitting the electron the greater the impact on its velocity.
11. There is yet another limitation to knowing the present sufficiently to forecast, first propounded by Edward Lorenz (1963), and popularly illustrated by the “butterfly effect.” Lorenz showed that for many nonlinear systems even the slightest error in measurement will be compounded over time to cause a forecast to veer increasingly off course.
12. Soros (1987). Also see Soros (2013) and related articles in that issue, and the first two lectures in Soros (2010).
13. And we can add to this Robert K. Merton’s (1948) concept of the self-fulfilling prophecy, which I will discuss in chapter 10.
14.

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A network is defined by connections, and network theory seeks to supply useful definitions of network complexity and analyze the stability of various network structures.
Nonlinearity and Complexity
Nonlinear systems are complex because a change in one component can propagate through the system to lead to surprising and apparently disproportionate effects elsewhere, for example, the famous “butterfly effect.” Indeed, as we first learned from Henri Poincaré’s analysis of the three-body problem in 1889, which later developed into the field of chaos theory, even simple nonlinear systems can lead to intractably complex results. The dominant and nearly inescapable form of nonlinearity for human systems is not strictly found in the social, organizational, or legal norms we follow, or in how people behave in a given environment; it is in the complexity of the dynamics, of the feedback cycle between these two. The readiest example of this nonlinearity is the prospect for emergent phenomena.

But he was more positive about the United States, calling it “a pragmatic nation that doesn’t give up easily, and has the determination and the optimism to keep trying new things until it solves a problem.” As for China, du Plessis had little doubt that its long-term growth rate remained in place, “keeping China firmly in position as the world’s primary engine of growth.”17
This is the human element of the Earth wars, but there is a natural element at play as well. In classic chaos theory, tiny differences at the start of a sequence of events lead to vastly different outcomes—the so-called butterfly effect popularised by the U.S. mathematician and meteorologist Edward Lorenz in his work on computerised weather prediction in the 1960s. Lorenz, a professor emeritus at Massachusetts University of Technology (MIT) when he died in 2008 at the age of 90, wrote a paper in 1972 titled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” to explain his theory of sensitive dependence on initial conditions.

By mathematically showing that there was no need in the astronomical world even for Newton’s Nudge God to intervene to keep the solar system stable, Laplace took away that skyhook. ‘I had no need of that hypothesis,’ he told Napoleon.
The certainty of Laplace’s determinism eventually crumbled in the twentieth century under assault from two directions – quantum mechanics and chaos theory. At the subatomic level, the world turned out to be very far from Newtonian, with uncertainty built into the very fabric of matter. Even at the astronomical scale, Henri Poincaré discovered that some arrangements of heavenly bodies resulted in perpetual instability. And as the meteorologist Edward Lorenz realised, exquisite sensitivity to initial conditions meant that weather systems were inherently unpredictable, asking, famously, in the title of a lecture in 1972: ‘Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?’
But here’s the thing.

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It remains at least a convenient fiction, a skyhook from which to hang the practical necessities of the criminal justice system among other things. Perhaps, muses Cashmore, we inherit a belief in free will.
These thinkers are in the tradition of determinism that goes back at least to Spinoza. But they escape the charge so often levelled at determinists, that they are fatalists. Remember the lesson of chaos theory, that tiny differences in initial conditions can result in hugely divergent outcomes. Given that every football match starts with the same number of players, roughly the same size of pitch, the same sort of ball and the same rules, is it not astounding that every game is unique? How much more unpredictable is a human life, full of chance encounters and missed opportunities? Even two identical twins reared in the same house and educated in the same school will still be somewhat different.

But the other half is
unhelpful, too. It is not — pace Marx — the surplus value stored up by
Mr. Moneybags (Herr Geldsack) that propels modern innovation. Such
profit is merely a hope tempting to the imagination. Profit comes mostly
from productivity, not as the pessimists of the left and right insist mostly
from monopoly. Paul Sweezy, Paul Baran, Stephen Marglin, William
Lazonick, Bernard Elbaum, Edward Lorenz, Jon Cohen, Robert Allen,
and other economic scholars on the left — an astonishing group, by the
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way, presenting a scientific challenge largely ignored by the
Samuelsonian/ Friedmanian orthodoxy in modern economics — have
been claiming for a long time that innovation was determined by the
struggle over the spoils (in a phrase, by monopoly capitalism), for good
[Galbraith, Lazonick] or evil [Baran and Sweezy]).

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What we are looking at is the
inception of something which was at first insignificant and even
bizarre,” though “destined to change the life of every man and woman in
the West.” 29 In the case of the Industrial Revolution now the East. Yet
one might wonder—the point will be made many times here in various
different ways—why then it did not happen before. “Sensitive
dependence on initial conditions” is the technical term for some
“nonlinear” models—a piece of so called “chaos theory.” But under such
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circumstances a history becomes untellable. 30 It may be so—the world
may be in fact nonlinear dynamic, as Basil Moore argues. But then we
will need to give up our project of telling its history, because the true
causes will consist of lost horseshoe nails and butterfly effects too small
to be detected. The reasons are the same as those that make it impossible
to forecast distant weather: “Current forecasts are useful for about five
days,” writes a leading student of such matters, “but it is theoretically
impossible to extend the window more than two weeks into the future.”
31
It is “theoretically” impossible because the fluid mechanics, the
radiative transfer, the photochemistry, the air-sea interactions, and so
forth “are violently non-linear and strongly coupled.”

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As Emerson noted, “an idealist can
never go backward to be a materialist.”3
A piling up of rejected alternatives, all of the same re-allocative
character, does suggest by sober scientific criteria that we may be
looking in the wrong place — perhaps under the lamppost of static
economics, or under a somewhat grander lamppost of a dynamics
depending on statics, or under the grandest lamppost discovered so far,
of a non-linear dynamics of chaos theory. Perhaps we are looking in such
places not because the evidence leads us to them but on account of the
excellent mathematical light shining under all these impressively
ornamented lampposts. Yet one after another of the proffered material
explanations has failed. No believable case can be made that adding
them all together would change much, or that other countries and other
times did not have equally favorable material conjunctures — not if we
are trying to explain the unprecedented factors of growing production
per head.

They’re relatively Newtonian: the uncertainty principle—interesting as it might be to physicists—won’t bother you much. You’ve gotten your hands on a state-of-the-art piece of equipment like the Bluefire. You’ve hired Richard Loft to design the computer’s software and to run its simulations. What could possibly go wrong?
How Chaos Theory Is Like Linsanity
What could go wrong? Chaos theory. You may have heard the expression: the flap of a butterfly’s wings in Brazil can set off a tornado in Texas. It comes from the title of a paper19 delivered in 1972 by MIT’s Edward Lorenz, who began his career as a meteorologist. Chaos theory applies to systems in which each of two properties hold:
The systems are dynamic, meaning that the behavior of the system at one point in time influences its behavior in the future;
And they are nonlinear, meaning they abide by exponential rather than additive relationships.

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After spending weeks double-checking their hardware and trying to debug their program, Lorenz and his team eventually discovered that their data wasn’t exactly the same: one of their technicians had truncated it in the third decimal place. Instead of having the barometric pressure in one corner of their grid read 29.5168, for example, it might instead read 29.517. Surely this couldn’t make that much difference?
Lorenz realized that it could. The most basic tenet of chaos theory is that a small change in initial conditions—a butterfly flapping its wings in Brazil—can produce a large and unexpected divergence in outcomes—a tornado in Texas. This does not mean that the behavior of the system is random, as the term “chaos” might seem to imply. Nor is chaos theory some modern recitation of Murphy’s Law (“whatever can go wrong will go wrong”). It just means that certain types of systems are very hard to predict.
The problem begins when there are inaccuracies in our data. (Or inaccuracies in our assumptions, as in the case of mortgage-backed securities).

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“I did a bold and stupid thing—I made a testable prediction. That’s what we’re supposed to do, but it can bite you when you’re wrong.”
Bowman’s idea had been to identify the root causes of earthquakes—stress accumulating along a fault line—and formulate predictions from there. In fact, he wanted to understand how stress was changing and evolving throughout the entire system; his approach was motivated by chaos theory.
Chaos theory is a demon that can be tamed—weather forecasters did so, at least in part. But weather forecasters have a much better theoretical understanding of the earth’s atmosphere than seismologists do of the earth’s crust. They know, more or less, how weather works, right down to the molecular level. Seismologists don’t have that advantage.
“It’s easy for climate systems,” Bowman reflected.

The scientific term for it is “sensitive dependence on initial conditions.” It is an aspect of chaos theory first studied by the meteorologist Edward Lorenz, who, while running computer simulations of weather patterns, discovered that the slightest change in the initial conditions of the simulation would quickly lead to completely different weather.
So the strong covering law model said that historical explanation should equal the rigor of scientific explanation. Then its defenders, bringing the model into the quantum world, conceded that predictions can never be anything but probabilistic at best. The explanandum was no longer deducible from the explanans; one could only suggest probabilities.
Now chaos theory has added new problems. And yet consider: Captain Frank January chose to miss Hiroshima.

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“The Lucky Strike”
One day in 1983, when we were living in our little place in downtown Davis, the image came to me of the Enola Gay, flying toward Japan but then tipping over and falling into the sea. That was a story for sure, but what? After a few weeks of reading I wrote it out pretty quickly.
“A Sensitive Dependence on Initial Conditions”
After I wrote “The Lucky Strike,” I began to have second thoughts about the postwar alternative history described at the end of that story. Back in DC after our Swiss adventure, I was reading all the new stuff about chaos theory, and some historiography in preparation for the Mars books, and it seemed to me human history might be regarded as a kind of chaotic system. This story was the result. It had a strange form, but it did what I wanted; and “form follows function” is one of the great rules.
“Arthur Sternbach Brings the Curveball to Mars”
This one I wrote in 1998, but the inspiration for it came from our two years in Zürich (1986–87), when I was a member of the baseball team Züri 85.